We note from Eqs. (REF )-() that the denominator of
those expressions is always positive. This is because the power \(c\) 
in the temperature dependence of the dissipation coefficient satisfies
\(-4 < c < 4\)  (see, e.g.,
Refs. [1]}, [2]}, [3]}). On the
other hand, the sign of the numerator in the above expressions will
depend on both the form of the dissipation coefficient and on the
inflaton potential exponent \(n\) . As examples of representative cases
of WI models, we can consider two cases of dissipation coefficient
that are well motivated microscopically: (a) \(c=1,\,p=0\) , i.e., a
linear in the temperature dependence for the dissipation coefficient,
\(\Upsilon \propto T\) , and that was first derived in
Ref. [4]} in the case of the WLI; and (b)
\(c=3,\,p=0\) , i.e., a cubic power in the temperature dependence for the
dissipation coefficient, \(\Upsilon \propto T^3\) , and derived recently
in Refs. [5]}, [6]} in the case of the MWI.
From the Eqs. (REF )-() we find that in case (a)
both \(Q\)  and \(T/H\)  are growing functions with the number of efolds
for \(n>1/3\)  for all \(c_s\) , while \(c_s\)  initially decreases for \(n<3\) 
when \(Q \ll 1\) , while for \(Q> 1\)  it will increase for \(n>13/7\)  and
decreases otherwise. In case (b) \(Q\)  and \(c_s\)  are decreasing
functions with the number of efolds whenever \(n<3\)  and \(c_s^2<1/3\)  or
\(n>3\)  and \(c_s^2> 1/3\)  and increasing functions with \(N\)  otherwise,
while \(T/H\)  is in general a growing function with \(N\) . Both cases (a)
and (b) then reinforces the WI condition \(T/H >1\)  throughout the
inflationary dynamics.
